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I've heard people make confident assertions about the categorical distinction between inference and deduction, but I'm not convinced.

I'm curious to hear rebuttals to the assertion that "inference is just tentative deduction."

As well as the distinction between certain conclusions and tentative ones, I believe some people may include consideration of the "direction" of reasoning as one of the distinctions between these processes. However, in a situation where I observe an effect and infer a cause, I think it's likely that reasoning follows both direction, in the sense that I may hypothesise a cause and then check if deduction tentatively confirms it. I expect that in the actual thought process of deduction and inference, both these directions are used.

So, is a categorical distinction between these two terms/processes logically justified? For bonus points, please highlight which your are using in your claims.

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  • "Inference", as far as I understand, is just a step in a reasoning, and can apply to both deductive reasoning and inductive reasoning. But it looks like you are referring to "deduction" and "induction"?
    – Frank
    Commented Jan 22, 2023 at 16:57
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    First, it's not clear from the question that you understand that deduction is a kind of inference. Second, there are many examples of non-deductive reasoning and you seem to be just assuming without justification that these examples can all be reduced to deduction. A proposition made without justification can be dismissed without justification. Commented Jan 22, 2023 at 17:07
  • Does this answer your question? What is the difference between inference and deduction?
    – Conifold
    Commented Jan 22, 2023 at 21:07
  • The Sun has risen each morning of my life, therefore it is likely it will do so tomorrow. Inference or deduction? We could have as one premise "things which have not yet failed to regularly occur are likely to continue that way," and then as long as we respect the "likelihood" component, we are in the realm of deduction, perhaps? It was mentioned above that "deduction is a kind of inference" but I believe I have read many claims otherwise. Could we also say "inference is a kind of deduction," and then maybe have set equality due to mutually inclusive subsets? Commented Jan 22, 2023 at 21:20
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    @RobinAndrews I think rather that "inference" in general refers to any step in a reasoning. You can infer a conclusion deductively or inductively. The terms that are opposed here are "deduction" and "induction" (not "inference"). The example with the sun is an inference by induction, although yes, if you add the premise you suggest, it starts behaving like a deduction. The point would be that in a deduction, the logical validity comes from the form of the argument.
    – Frank
    Commented Jan 23, 2023 at 3:40

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If you are referring to "deduction" and "induction", which are two modes of reasoning ("abduction" would be a third one), the difference lies in the methodology they use.

Deduction relies on (formal/informal) logic to infer conclusions from premises - there are strict rules that you have to follow, and those rules guarantee that the reasoning will not lead to a contradiction. For example: "all men are mortals, Socrates is a man, therefore Socrates is mortal" is a deductive inference, with 2 premises that entail a conclusion. The argument is said to be "valid" because it follows a rule of logic that guarantees the conclusion is true if the premises are true (in some sense). Deduction is paradigmatically used in mathematics when presenting proofs of theorems (not necessarily in the day to day work of the mathematician!).

Induction relies on a different mechanism to validate its claims. Here, the accumulation of observations is presented as support for the conclusion. For example: we have observed that the Sun rises in the East every morning for 10,000 years, therefore it will rise in the East tomorrow morning. From a formal logical standpoint, there is no valid deduction that would guarantee the conclusion. But it still seems very reasonable to assert the conclusion. Induction is used in physics (but physics can also use deduction!). Induction does not have the same strength as deduction, in the sense that a contradictory observation tomorrow morning may destroy the conclusion.

A few more things. Physics routinely uses both induction, deduction, abduction and whatever other form of reasoning will be helpful, and mathematicians in day to day work may well use induction, ... However, when results are presented officially, a mathematician would typically be required to submit a proof relying on deduction from axioms in their published paper - it is the accepted standard of confirmation in the field, and a physicist would have to present their observations in the discovery paper, as this is the accepted standard of confirmation in that field. A physicist who would deduce e.g. the existence of a particle but with no experimental (inductive) confirmation, would only have a hypothesis. A mathematician who had only observations about e.g. some behavior of prime numbers would have only a conjecture till they can present a deductive proof. And both physicists and mathematicians are trained to be very parsimonious and careful in their claims and to not overstep the bounds of what is hypothesis/conjecture and what has the status of "knowledge".

And one more thing. Deductive reasoning based on logic only guarantees that the argument is valid, i.e. that true premises will not lead to a false conclusion. But it doesn't weigh in on the actual veracity of these premises with respect to the world. You can feed non realistic premises into the logic machinery and correctly deduce non-realistic conclusions all day long. "All dogs are blue, Rex is a dog, therefore Rex is blue" is a flawless logical deduction. So, deduction offer certainty in reasoning, but in itself is not a guarantee that you reach any knowledge about the world. Induction on the other hand attempts to reach knowledge about the world, but in so doing, it is forever uncertain, as we do not know what observation will defeat it tomorrow.

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